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An aquarium has a regular hexagonal base with side lengths of 15 centimeters. When the hexagon is divided into six equal triangles, the height of each triangle is about 13 centimeters. If the aquarium is 50 centimeters tall, what is its volume?

Respuesta :

calculista

Answer:

[tex]V=29,250\ cm^3[/tex]

Step-by-step explanation:

we know that

The volume of a hexagonal prism is given by the formula

[tex]V=Bh[/tex]

where

B is the area of the hexagonal base

h is the height of the aquarium

we have

[tex]h=50\ cm[/tex]

[tex]B=6[\frac{1}{2}(15)(13)]= 585\ cm^2[/tex]

substitute

[tex]V=585(50)=29,250\ cm^3[/tex]

The volume of the aquarium should be [tex]29,250\ cm^3[/tex].

Calculation of the  volume of the aquarium:

Since

The volume of a hexagonal prism should be

V = Bh

Here

B is the area of the hexagonal base

h is the height of the aquarium

So

= 50(585)

= 29,250

Hence, The volume of the aquarium should be [tex]29,250\ cm^3[/tex].

Learn more about volume here: https://brainly.com/question/12497184

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